@BillRM,
Quote:Quote:Wow. Would you mind describing or diagramming the force and energy balances that bring you to this conclusion?
I will let you go first and after you get done with that task you can show how a weight hanging from a pulley can go upward.
Vt = true wind velocity wrt ground, downwind
Vc = cart velocity wrt ground, upwind
Force balance:
Fp = force of wind on prop, pushing cart backward
Fq = drag and friction forces (small by design), pushing cart backward
Fg = force of wheels on ground, pushing cart forward (Newton 3)
At steady state, forces forward = forces backward, no acceleration:
Fg = Fp + Fq
Power balance:
Pp = power obtained from prop = Fp * (Vt+Vc), input
Pq = power losses (again small by design), output
Pg = power applied to ground, output = Fg * Vc
At steady state, power inputs = power outputs, no accumulation:
Pp = Pg + Pq
also
Fp * (Vt+Vc) = Fg * Vc + Pq
rearranging
Fp * Vt = (Fg - Fp) * Vc + Pq
substituting Fq for (Fg - Fp)
Fp * Vt = Fq * Vc + Pq
and finally solving for the speed ratio:
Vc / Vt = (Fp - Pq/Vc) / Fq
so both balances can be satisfied simultaneously with Vc/Vt positive or even over one if losses (Pq and Fq) are kept low enough; keeping the losses low is a design hurdle, not a fundamental theoretical hurdle. Getting Fg up to the necessary level is only a matter of gearing (design) because input power from Fp is available at (Vt+Vc) while the output drive power to the wheels is applied at the larger Fg but at only Vc. Note also that as the design Vc/Vt or as Vt goes up so do Fq and Pq which makes it harder satisfy that last equation, so this is not an over-unity system.
Your weight and pully thought experiment is another irrelevant analogy.